PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 3.6, Problem 32E

To determine

To determine the regression feature of a graphing utility to attempt to find the logarithmic model and explain why the result is an error message.

Expert Solution

Answer to Problem 32E

The logarithmic model p=a+blnh you will get an error because of the point (0,1).

Explanation of Solution

Given:

Consider the given information,

p=a+blnh

and the data provided are (0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

For the given data, it is understood that the point (0,1) has an error because from the given expression if (h, p) = (0,1) then it is clear that 0 is not in the domain of ln.

To determine

To determine the regression feature of the graphing utility to find the logarithmic model for the data.

Expert Solution

Answer to Problem 32E

The logarithmic model for the data is h=0.863−6.44lnp

Explanation of Solution

Given:

Consider the given expression,

p=a+blnh

Graph:

Calculation:

From the given expression,

Reversing the expression, it can be written as h=a+blnp of the order of (h, p)

As, h=0.863−6.44lnp

Conclusion:

Therefore, the logarithmic model is h=0.863−6.44lnp .

To determine

To graph: using graphing utility to plot the data and the logarithmic model in the same viewing window.

Expert Solution

Explanation of Solution

Given information: Consider the data given,

(0,1),(10,0.25),(20,0.06),(5,0.55),(15,0.12),(25,0.02)

Graph:

Interpretation: as from the following graph, it is clear that the data is fitted with the logarithmic model.

To determine

To estimate the altitude using the model at a given pressure.

Expert Solution

Answer to Problem 32E

The altitude at a given pressure using the model is ≈2.7km .

Explanation of Solution

Given:

Consider the given information,

Pressure of the model is 0.75 atmosphere.

Calculation:

From the given data,

Pressure = 0.75atm

Altitude = 0.863-6.447 ln(0.75)

≈2.7km

Conclusion:

Therefore, the altitude of the model is ≈2.7km

To determine

To estimate the pressure at an altitude of given kilometer.

Expert Solution

Answer to Problem 32E

The pressure at the altitude given is 0.15 atmosphere.

Explanation of Solution

Given:

The altitude for the model given is 13km.

Calculation:

From the graph, at altitude = 13km the pressure is 0.15 atmosphere.

Chapter 3.6, Problem 31E

Chapter 3.6, Problem 33E

Chapter 3 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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Prob. 111CR Ch. 3 - Prob. 112CR Ch. 3 - Prob. 113CR Ch. 3 - Prob. 114CR Ch. 3 - Prob. 115CR Ch. 3 - Prob. 116CR Ch. 3 - Prob. 117CR Ch. 3 - Prob. 118CR Ch. 3 - Prob. 119CR Ch. 3 - Prob. 120CR Ch. 3 - Prob. 121CR Ch. 3 - Prob. 122CR Ch. 3 - Prob. 123CR Ch. 3 - Prob. 124CR Ch. 3 - Prob. 125CR Ch. 3 - Prob. 126CR Ch. 3 - Prob. 1CT Ch. 3 - Prob. 2CT Ch. 3 - Prob. 3CT Ch. 3 - Prob. 4CT Ch. 3 - Prob. 5CT Ch. 3 - Prob. 6CT Ch. 3 - Prob. 7CT Ch. 3 - Prob. 8CT Ch. 3 - Prob. 9CT Ch. 3 - Prob. 10CT Ch. 3 - Prob. 11CT Ch. 3 - Prob. 12CT Ch. 3 - Prob. 13CT Ch. 3 - Prob. 14CT Ch. 3 - Prob. 15CT Ch. 3 - Prob. 16CT Ch. 3 - Prob. 17CT Ch. 3 - Prob. 18CT Ch. 3 - Prob. 19CT Ch. 3 - Prob. 20CT Ch. 3 - Prob. 21CT Ch. 3 - Prob. 22CT Ch. 3 - Prob. 23CT Ch. 3 - Prob. 24CT Ch. 3 - Prob. 25CT Ch. 3 - Prob. 26CT Ch. 3 - Prob. 27CT Ch. 3 - Prob. 28CT Ch. 3 - Prob. 29CT Ch. 3 - Prob. 30CT Ch. 3 - Prob. 1STP Ch. 3 - Prob. 2STP Ch. 3 - Prob. 3STP Ch. 3 - Prob. 4STP Ch. 3 - Prob. 5STP Ch. 3 - Prob. 6STP Ch. 3 - Prob. 7STP Ch. 3 - Prob. 8STP Ch. 3 - Prob. 9STP Ch. 3 - Prob. 10STP Ch. 3 - Prob. 11STP Ch. 3 - Prob. 12STP Ch. 3 - Prob. 13STP Ch. 3 - Prob. 14STP Ch. 3 - Prob. 15STP Ch. 3 - Prob. 16STP Ch. 3 - Prob. 17STP Ch. 3 - Prob. 18STP Ch. 3 - Prob. 19STP Ch. 3 - Prob. 20STP Ch. 3 - Prob. 21STP Ch. 3 - Prob. 22STP Ch. 3 - Prob. 23STP Ch. 3 - Prob. 24STP Ch. 3 - Prob. 25STP Ch. 3 - Prob. 26STP

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